We present in this paper a new reliable and efficient 4-node quadrilateral element, which we call the 2D-MITC4 element, for two-dimensional plane stress and plane strain solutions of solids using the MITC method. We also present an extension of the element assuming a constant element pressure, which we call the 2D-MITC4/1 element. The elements show a much better predictive capability than the displacement-based element and perform in linear analyses almost as well as the 4-node element with incompatible modes, an enhanced assumed strain (EAS) element. However, unlike when using EAS elements, we do not observe spurious instabilities in geometrically nonlinear solutions. Embedding the new MITC formulation into the previously presented MITC4+ shell element, we improve the membrane behavior of the shell element. The new 2D solid elements and the improved MITC4+ shell element pass all basic tests (the isotropy, zero energy mode and patch tests). We present the finite element solutions of various benchmark problems to illustrate the solution accuracy of the new elements. (C) 2017 Elsevier Ltd. All rights reserved.